<![CDATA[In this paper, we investigate an investor’s portfolios in a defined contributory (DC) Pension Scheme with return of contributions for a mortgage housing scheme and managerial fees for time-inconsistent utility. A portfolio with a fixed deposit (risk-free asset) and two stocks (risky assets) is taken into consideration, where the stock market prices of the risky assets follow the geometric Brownian motion (GBM) and the instantaneous volatilities form a positive definite matrix. To determine the number of scheme members (SM) interested in the mortgage housing, the Abraham De Moivre function is used. Furthermore, the dynamic programming and game techniques were used to obtain our optimization problem by maximizing the expected utility (mean-variance utility) subject to the SM’s wealth. Using the variable change technique, the optimal value function (OVF), investor’s optimal plan (IOP), and the efficient frontier were obtained under mean variance utility function. . Furthermore, some numerical results of some sensitive parameters such as risk-free interest rate (RIR), risk averse coefficient (RAC), entry age (EA) of SM, managerial charges (MC), optimal fund size (OFS), instantaneous volatilities (IV) and appreciation rates (AR) of the risky assets were presented to explain their impact on the IOP. It was observed that the IOP, which is the fraction of SM’s accumulations invested in the risky assets, is a decreasing function of RIR, RAC, IV, EA, OFS, and MC but an increasing function of the AR.]]>
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